# How to find the standard form of the equation of the specified circle given Center: (0,0); Radius: 9?

Mar 21, 2018

${x}^{2} + {y}^{2} = 81$

#### Explanation:

The standard form for the equation of a circle with center $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$ and radius $\textcolor{m a \ge n t a}{r}$ is
$\textcolor{w h i t e}{\text{XXX}} {\left(x - \textcolor{red}{a}\right)}^{2} + {\left(y - \textcolor{b l u e}{b}\right)}^{2} = {\textcolor{m a \ge n t a}{r}}^{2}$

Mar 21, 2018

${x}^{2} + {y}^{2} = 81$

#### Explanation:

$\text{the standard form of the equation of a circle is}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where "(a,b)" are the coordinates of the centre and r is}$
$\text{the radius}$

$\text{here "(a,b)=(0,0)" and } r = 9$

$\Rightarrow {\left(x - 0\right)}^{2} + {\left(y - 0\right)}^{2} = {9}^{2}$

$\Rightarrow {x}^{2} + {y}^{2} = 81 \leftarrow \textcolor{red}{\text{in standard form}}$